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On the slow broadside motion of a thin disc along the axis of a fluid-filled circular duct

Published online by Cambridge University Press:  24 October 2008

R. Shail  and
D. J. Norton
R. Shail
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey
D. J. Norton
Affiliation:
Department of Mathematics, University of Surrey, Guildford, Surrey
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Extract

The study of the slow motion of a solid body through a viscous fluid is of importance in many fields. We may instance viscometry and chemical engineering as two subjects in which a quantitative understanding of such motions is essential. Thus, in recent years systematic attempts have been made to calculate the drag force and couple on slowly sedimenting particles in a bounded viscous fluid. Using the ‘method of reflexions’ Brenner (1) has obtained formulae which give, for a wide class of sedimenting particles, an estimate of the effect of the container walls on the drag force, the error being O(c/l)3, where c is a characteristic particle dimension and l the distance from the centre of the particle to the nearest boundary wall. The reader is referred to the recent book by Happel and Brenner (2) for a complete account of these and other pertinent investigations; also to Williams (3) for an alternative integral equation approach to these results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 65 , Issue 3 , May 1969 , pp. 793 - 802
Copyright
Copyright © Cambridge Philosophical Society 1969

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References

REFERENCES

(1)Brenner, H.J. Fluid Mech. 12 (1962), 35.CrossRefGoogle Scholar
(2)Happel, J. and Brenner, H.Low Beynolds number hydrodynamics (Prentice Hall, 1965).Google Scholar
(3)Williams, W. E.J. Fluid Mech. 24 (1966), 285.CrossRefGoogle Scholar
(4)Bohlin, T.Trans. Roy. Inst. Technol. (Stockholm), no. 155 (1960).Google Scholar
(5)Haberman, W. L. and Sayre, R. M.David Taylor model basin report, no. 1143 (1958).Google Scholar
(6)Faxen, H.Ark. Mat. Astron. Fys. 17, no. 27 (1923).Google Scholar
(7)Squires, L. and Squires, W.Amer. Inst. Chem. Engrg 33 (1937), 12.Google Scholar
(8)Sneddon, I. N.Mixed boundary value problems in potential theory (North Holland, 1966).Google Scholar
(9)Green, A. E. and Zerna, W.Theoretical elasticity (Oxford University Press, 1954).Google Scholar
(10)Shaxl, R.Internal. J. Engrg Sci. 3 (1965), 597.Google Scholar
(11)Gupta, S. C.Z. Angew. Math. Phys. 8 (1957), 257.CrossRefGoogle Scholar
(12)Erdelyi, A. et al. Tables of integral transforms, vol. 2 (McGraw-Hill, 1954).Google Scholar
(13)Watson, G. N.Theory of Bessel functions (Cambridge, 1966).Google Scholar
(14)Sonshine, R. M., Cox, R. G. and Brenner, H.Appl. Sci. Res. 16 (1966), 325.CrossRefGoogle Scholar
(15)Wakiya, S. J.J. Phys. Soc. Japan 12 (1957), 1130.CrossRefGoogle Scholar
(16)Fox, L. and Goodwin, E. T.Philos. Trans. Roy. Soc. London, Ser. A, 245 (1953), 501.Google Scholar
(17)Happel, J. and Ast, P. A.Chem. Eng. Sci. 11 (1960), 286.CrossRefGoogle Scholar